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Simulating the Cosmic Web

The beautiful tapestry of filaments, sheets, and voids in the Cosmic Web is proving harder to model than anybody thought.

December 21, 2009

The idea that stars clump together in “island universes”
is relatively new to astronomy. It was only in the 1920s and ’30s that
astronomers agreed among themselves that “galaxies” must be
separated by vast distances.

But only in the last 10 years or so have astronomers discovered
that galaxies themselves form into a far larger structure. The 100
billion galaxies that we know about are woven into a wispy web-like
arrangement consisting of dense compact clusters, elongated filaments
and sheet-like walls, amid large near-empty void regions.

This structure has become known
as the Cosmic Web and one of the great challenges in modern
cosmology is to accurately model and simulate it.

That’s turning out to be tricky.

One of the important features of the Cosmic Web is that its
structures range over many orders of magnitude. And since the largest
structures, such as the wall-like features, are formed out of the
smaller ones such as filaments and clusters, it’s crucial that any
model can handle the relationship between them at
all these scales.

That’s easier said than done. One way to imagine the problem is to
think about zooming out from a particular cluster of galaxies to show
the larger structures, rather in the manner of the famous Powers of
Ten movie made in the 1970s.

As the small scale structures become too
small to resolve, most computer models apply some kind of
statistical smoothing process to make the large scale calculations
easier.

But if you zoom back in again, there is no way to retrieve the
information that is lost by the smoothing process, other than to
rebuild the picture again from the original data.

That’s okay if all you want is a 3-D model of the universe. But it’s
a problem if you want to simulate how the large scale structures form
from smaller structures and how, in turn, the shape of the large
structures influences the way smaller structures evolve.

This kind of feedback process is impossible to model when the
smoothing process between different scales essentially destroys any
meaningful links between them.

Enter Rien van de Weygaert and Willem Schaap at the University of
Groningen in the Netherlands. These guys have developed a way of
modeling structures over many scales without the unnatural smoothing
that other approaches use.

Their trick is to think of galaxies as points in 3D space and to
fill the space between them with tetrahedra. These tetrahedra must be
constructed in such a way that, if a sphere were inflated inside each
one until it touched the sides, there would be no galaxies inside
each sphere.

This is known as a Delauney tessellation. What’s special about
Delauney tessellations is that as the scale gets larger, there are
rules for combining the tetrahedra into larger ones. These
rules are special because they are reversible, meaning that the
important features of the original structure can be reconstructed
when you zoom in again.

That makes it much easier to simualte the feedback between structures on various scales.

So it’s no surprise that astronomers are excited about the
potential of the so-called Delaunay Tessellation Field Estimator
(DTFE). If you want to know more, de Weygaert and a few mates give a
comprehensive outline of the idea on the arXiv today.

It should mean that we’ll have a much better model of the large
scale structure of the universe.

It should also mean that we can update the Powers of Ten movie
which, understandably given its age, shows no detail in the universe beyond our local cluster of
galaxies.

Ref: arxiv.org/abs/0912.3448:
Geometry and Morphology of the Cosmic Web: Analyzing Spatial Patterns
in the Universe

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